the Use of Brackets
You have learned to carry out the operations of addition, subtraction, multiplication, and division. Let us study these operations further. Consider the following examples :
Ex (1) Simplify : 75 + 25 x 10
Addition and multiplication are the two operations in this example.
If we carry out the addition 75 + 25 first, the value of this expression will be 100 x 10 = 1000
If we carry out the multiplication 25 x 10 first, then the value of the expression w
We shall have to say that the same expression has two different values. It is obvious that this will cause confusion.
Use of Brackets
It is necessary to know which operation should be carried out first in order that the expression yields a single value. Brackets are used for this purpose. The operation to be carried out first is written inside brackets.
For example, if the addition is to be carried out first in the expression 75 + 25 x 10, then the expression is written as (75 + 25) x 10.
If the expression is 75 +(25x10), multiplication will be carried out first.
The value of the expression (75 + 25 ) x 10 is 1000.
And the value of 75 + (25 x 10 ) is 325.
Similarly, ( 48 ÷ 8 ) ÷ 2 = 3 and 48 ÷ ( 8 ÷ 2 ) = 12.
The following rules are generally
followed to minimize the use of
brackets in an expression.
(1) Operations in brackets should be carried out first.
(2) After that, multiplication and division must be carried out in the order in which they occur from left to right.
(3) Then, addition and subtraction should be carried out in the order in which they occur from left to right.
(4) If there are more than one operations inside a bracket, they are carried out first, following rules 2 and 3.
